Finite Group Databasebeta

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D3×#72213282 #72259768

order19200
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C29

Aliases

direct productD3×#72213282

Splittings

FittingC2×C3×C52×D4 ⋊ C22×C4
HallC3×C52 ⋊ C2×C4×AGL(1,ℤ/8)
SylowC52 ⋊ C4×D3×AGL(1,ℤ/8)
SylowC3 ⋊ C2×#72213282

Subgroups

subgroupG/H
centerC2C2×D3×#11717375
commutatorC3×C4×C52C24×C4
FrattiniC4C22×D3×D5⋊AGL(1,𝔽5)
FittingC2×C3×C52×D4C22×C4
socleC2×C3×C52C22×C4×D4
prime radicalD3×#13106298C2
cosocleC3×C4×C5⋊D5C25
hypercenterC2×D4D3×D5⋊AGL(1,𝔽5)
hypocenterC3×C52C2×C4×AGL(1,ℤ/8)
LCSG ▷ C3×C4×C52 ▷ C2×C3×C52 ▷ C3×C52
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×D4

18024 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 120

Conjugacy classes & character table

258 conjugacy classes. The character table is too large to display.

Relationships

holomorph ofC3×#168

GAP

Past the SmallGroups library coverage — no SmallGroups id.